- 2^17 - 1 = 131071. Both 131 and 071 are prime, or 131~071,
or 3~(2^17-1), since it splits at the third position.
I tried to split other Mersenne primes up into two primes,
but found no other examples up to 2^9689 - 1.
What is the largest known splitable prime?
-Ed Pegg Jr
- --- In email@example.com, "newjack56" <mrnsigepalum@a...>
> I have a quick question. How did Lucas determine s of 0 =4? The
> am reading says he uses U of n and V of n for (P,Q). IF (P,Q)help!!
> determines that s of 0 =4, Which equation did he use or which (P,Q)
> did he use? Or, is 4 used because it is the first composite number.
> Because if you use 2 or 3, you get prime numbers. Thanks for any
Take a look at this paper :
You will understand that in fact, S0=4 is one possibility but that
there are in fact infinitely many others (look at theorem 4 on page
For example, S0=10 or S0=52 or S0=724 work as well.
- Ed Pegg Jr wrote:
> 2^17 - 1 = 131071. Both 131 and 071 are prime, or 131~071,I have not heard of searches for large splitable primes.
> or 3~(2^17-1), since it splits at the third position.
> What is the largest known splitable prime?
One way to search them is to concatenate known primes.
27918*10^10000+1 was found in 1999 by Yves Gallot.
58789 is the smallest prime which can be put in front and give a prime:
D:>pfgw -t -q"5878927918*10^10000+1"
PFGW Version 1.2.0 for Windows [FFT v23.8]
Primality testing 5878927918*10^10000+1 [N-1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Calling Brillhart-Lehmer-Selfridge with factored part 69.83%
5878927918*10^10000+1 is prime! (26.4531s+0.0023s)
The form k*10^n+1 was chosen to make the concatenation easily provable.
PrimeForm/GW prp tested and APTreeSieve sieved.
Jens Kruse Andersen
- I found two more splitable primes, 127,031 (127)(031) and 839809
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